Erratum: Entanglement and density-functional theory: Testing approximations on Hooke’s atom [Phys. Rev. B77, 205122 (2008)]

Abstract

In the subsection "Comparison to standard perturbation theory" the expression for the total energy of Hooke's atom to first order should readConsequently results for the error in energy from standard first-order perturbation ͓dotted curve in Fig. 13 ͑see Fig. 1 below͔͒ are modified.Standard first-order perturbation still has the lowest accuracy and no other results are affected.In addition: ͑i͒ In the last equation of the subsection "Position-space information entropy" the constant term in the expression for S when neglecting off-diagonal terms should read ln N / ln 2 instead of 1 / ln 2;͑ii͒ The y-axis in Fig. 5 and Fig. 12 should be labeled S n / ln 2; ͑iii͒ In the sixth paragraph of the section "Overview and Conclusions" it should be տ 0.03, instead of տ 0.003. The results and conclusions of the paper remain unaffected. Energy % Error ω (Hartrees) 0 10 20 30 40 50 0.001 0.01 0.1 1 LDA Perturbed LDA KS Perturbed Exact KS Standard Perturbation FIG. 1. Relative error of the approximate energy from LDA, first-order perturbation of the LDA KS equations, first-order perturbation of the exact KS equations and standard first-order perturbation, compared to the exact energy plotted against .

Benchmark calculations on the lowest-energy singlet, triplet, and quintet states of the four-electron harmonium atom

“…The extraction of natural spinorbitals and their occupation numbers {n i (ω)} from the approximate wavefunctions [Eq. (10)], and the subsequent derivation of the correlation measures, namely, the index of almost idempotency, 27,28 …”

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

“…In particular, a few attempts have been made recently towards understanding the entanglement in systems of interacting particles. For example, some light has been shed on entanglement both in quantum dot systems [6][7][8][9][10][11][12][13][14][15] and in systems of harmonically interacting particles in a harmonic trap (the so-called Moshinsky atom) [16][17][18][19][20][21][22][23]. Special attention has also been paid to the study of entanglement in the helium atoms and helium ions [24][25][26][27][28][29][30][31][32].…”

Magnetic alteration of entanglement in two-electron quantum dots

“…The same con-veniences also hold while calculating appropriate entanglement measures. The spatial entanglement measures have been used to test the validity of approximations of the density-functional theory for Hook's atom [26]. It represents a possible model for describing two electrons trapped in a quantum dot.…”